incidence matrix:
[[ 1.  0.  0.  0. -1.  0.]
 [ 0.  1.  0.  0. -1.  0.]
 [ 0.  0.  1.  0.  0. -1.]
 [ 0.  0.  0.  1.  0. -1.]
 [ 0.  0.  0.  0.  1. -1.]]

reference branch lengths:
[ 1.10047901  0.18570314  0.48115285  1.05849769  2.37489145]

centered covariance matrix for the reference branch lengths:
[[ 1.32057691  0.44879187 -0.81251629 -0.9568525 ]
 [ 0.44879187  0.86318897 -0.58382232 -0.72815853]
 [-0.81251629 -0.58382232  1.01091383  0.38542477]
 [-0.9568525  -0.72815853  0.38542477  1.29958625]]

test branch lengths:
[ 0.8664449   0.27201223  0.28129483  1.08485675  5.94596636]

cross entropy:
4.56607962074

sampling a bunch of data...

sample data covariance matrix:
[[ 1.31769524  0.44591047 -0.80975888 -0.95384683]
 [ 0.44591047  0.86340588 -0.58334058 -0.72597577]
 [-0.80975888 -0.58334058  1.01089956  0.3821999 ]
 [-0.95384683 -0.72597577  0.3821999   1.2976227 ]]

average log likelihoods:
-4.56869723934

gradient of cross entropy:
[-0.05854639 -0.01943114 -0.03443427 -0.04078485 0.0428304 ]

hessian of cross entropy:
[[  4.97582035e-01   4.63804250e-01   4.88878348e-04  -1.08723293e-05  5.62837524e-04]
 [  4.63804250e-01   5.07361276e-01  -3.16744791e-04  -4.65100077e-04 -2.65770425e-03]
 [  4.88878348e-04  -3.16744791e-04   4.02400603e-01   3.32841627e-01  1.62992650e-03]
 [ -1.08723293e-05  -4.65100077e-04   3.32841627e-01   3.33038731e-01 -6.56618008e-04]
 [  5.62837524e-04  -2.65770425e-03   1.62992650e-03  -6.56618008e-04 -1.13641266e-03]]

eigenvalues of hessian of cross entropy:
[-0.00134004  0.03313779  0.03877968  0.70236462  0.96630417]

minimizing cross entropy...

branch lengths at minimum:
[ 1.10047688  0.18569188  0.48108829  1.05858838  2.3742567 ]

minimum cross entropy:
4.43149459225

gradient at minimum:
[ -4.52529508e-06  -3.58763508e-05  -2.49821793e-05   6.70903445e-06 -4.05207841e-05]

hessian at minimum:
[[  3.07947920e-01   2.69648831e-01   6.00973212e-04   1.24067924e-04 1.27116018e-03]
 [  2.69648831e-01   5.33753118e-01   2.11096999e-02   4.35799255e-03 4.46505931e-02]
 [  6.00973212e-04   2.11096999e-02   3.31782426e-01   1.64997661e-01 2.88342576e-02]
 [  1.24067924e-04   4.35799255e-03   1.64997661e-01   2.33629845e-01 5.95268903e-03]
 [  1.27116018e-03   4.46505931e-02   2.88342576e-02   5.95268903e-03 6.09893418e-02]]

eigenvalues of hessian at minimum:
[ 0.04869748  0.10964552  0.13732916  0.45567661  0.71675389]